Labour has challenged David Cameron to sort out the existing "welfare chaos" before starting any further shakeup of the system.

The opposition call came as the prime minister delivered a speech on the welfare system, setting out plans to cut housing benefits for under-25s and reduce benefits to out-of-work families after the birth of their third child.

Iain Duncan Smith, the work and pensions secretary, said the prime minister's speech was an attempt to invite discussion about what people "genuinely think on the back of what we have changed" in this parliament, such as universal credit, benefit reforms and work programmes.

But Liam Byrne, the shadow work and pension secretary, said the government should focus on sorting out the reforms already underway, which were designed to deliver "massive savings" and an improved welfare system but were "either failing or mired in chaos".

Labour revealed analysis from the House of Commons library that shows initial government estimates of Department for Work and Pensions (DWP) spending on jobseeker's allowance and housing benefit have been revised upwards by £9.1bn — an increase the opposition blames on the failure of the government's Work Programme to tackle unemployment.

It also pointed to the government decision to delay the introduction of universal credits, which requires two major IT programmes for it to be delivered. Costs have already soared by £100m, according to Labour.

Byrne said Cameron should sort out the mess before he planned any more "revolutions".

"David Cameron has put worklessness to a record high and he's inviting us to believe that it's the fault of everyone except him. It's now very clear that a welfare revolution was all talk. Out-of-work benefits are going through the roof. Each week we hear of another new initiative, another crackdown, another test.

"Meanwhile in the real world, the cost of out-of-work benefits is up nearly £5bn, housing benefit over £4bn, the Work Programme is failing and the multibillion-pound universal credit scheme is running late and over budget.

"Welfare spending is going up under this government because too many people are out of work, but at the last budget the chancellor's priority was not help to get people into work but a tax cut for millionaires."

Cameron acknowledged that some of the proposals could not be delivered in coalition with the Liberal Democrats, and would have to wait until a Conservative majority government was elected.

"I am exploring these issues not just as leader of a coalition but as a leader of the Conservative party who is looking ahead to the programme we will set out to the country at the next election," the prime minister said in his speech.

Chris Grayling, the employment minister, said the welfare state should be "a ladder up which you climb", not "a place in which you live".

He told ITV Daybreak: "A welfare state should be a safety net. It should be there to help you when you run into difficult times, when you lose your job, when you become sick – it's not a be-all-and-end-all in all circumstances."

But the consequences of removing housing benefit from young workers living in areas with high living costs, such as London, were highlighted by Darren Johnson, a Green party member of the London assembly.

Johnson warned that such a move could leave young workers priced out of all but a handful of areas in a city where average rents for a room in a shared flat are only affordable for a young person on the national minimum wage in four out of 33 boroughs.

"The prime minister's plans would just price young people out of work in London," he said. "They desperately need more jobs, higher wages and lower rents. You don't give a 24-year-old a sense of independence and responsibility by making it impossible to pay the rent on a room in a shared flat while keeping down a job.

"The government and the mayor urgently need to rethink their welfare and housing policies to support young workers instead of punishing them for living in a world of high rents and low wages."